We investigate a certain class of (geometric) finite (Galois) coverings of formal fibres of $p$-adic curves and the corresponding quotient of the (geometric) etale fundamental group. A key result in our investigation is that these (Galois) coverings can be compactified to finite (Galois) coverings of proper $p$-adic curves. We also prove that the maximal prime-to-$p$ quotient of the geometric etale fundamental group of a (geometrically connected) formal fibre of a $p$-adic curve is (pro-)prime-to-$p$ free of finite computable rank.
{"title":"On étale fundamental groups of formal fibres of $p$-adic curves","authors":"Mohamed Saidi","doi":"10.2748/tmj/1585101621","DOIUrl":"https://doi.org/10.2748/tmj/1585101621","url":null,"abstract":"We investigate a certain class of (geometric) finite (Galois) coverings of formal fibres of $p$-adic curves and the corresponding quotient of the (geometric) etale fundamental group. A key result in our investigation is that these (Galois) coverings can be compactified to finite (Galois) coverings of proper $p$-adic curves. We also prove that the maximal prime-to-$p$ quotient of the geometric etale fundamental group of a (geometrically connected) formal fibre of a $p$-adic curve is (pro-)prime-to-$p$ free of finite computable rank.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69220711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ming-Lun Hsieh constructed three-variable triple product p-adic L-functions attached to triples of primitive Hida families and proved interpolation formulas. We generalize his result in the unbalanced case and construct a three-variable triple product p-adic L-function attached to a primitive Hida family and two more general p-adic families of modular forms.
{"title":"Triple product $p$-adic $L$-function attached to $p$-adic families of modular forms","authors":"Kengo Fukunaga","doi":"10.2748/tmj.20210501","DOIUrl":"https://doi.org/10.2748/tmj.20210501","url":null,"abstract":"Ming-Lun Hsieh constructed three-variable triple product p-adic L-functions attached to triples of primitive Hida families and proved interpolation formulas. We generalize his result in the unbalanced case and construct a three-variable triple product p-adic L-function attached to a primitive Hida family and two more general p-adic families of modular forms.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43535706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dans cette courte note, on remarque qu’une petite modification dans le calcul effectue dans [5] de l’algebre du torseur d’isomorphismes entre la realisation de Betti tangentielle et la realisation de De Rham resulte en un enonce du type Kontsevich–Zagier fonctionnel purement algebrique et nettement plus satisfaisant que l’enonce obtenu dans [5].In this short note, we remark that a small modification in the computation made in [5] of the algebra of the torsor of isomorphisms between the tangential Betti realisation and the De Rham realisation results in a statement of functional Kontsevich–Zagier type which is purely algebraic and much more satisfactory than the statement obtained in [5].
在这个简短的注释中,可以看到一小在微积分中[5]进行变更的l’algebre torseur d’isomorphismes之间实现poncelet Betti切和de Rham Kontsevich型出现在一个国家—纯功能性Zagier algebrique和远比l’enonce[5]中获得令人满意的。肖特In this, we,在于说明that In the small更改计算了made In algebra》[5]“torsor isomorphisms between the Betti poncelet tangential and the De Rham成就——《results In a functional Kontsevich—Zagier型which is purely algebraic and much more than the做出满意的声明应该乐意In[5]。
{"title":"La version relative de la conjecture des périodes de Kontsevich-Zagier revisitée","authors":"J. Ayoub","doi":"10.2748/tmj/1568772181","DOIUrl":"https://doi.org/10.2748/tmj/1568772181","url":null,"abstract":"Dans cette courte note, on remarque qu’une petite modification dans le calcul effectue dans [5] de l’algebre du torseur d’isomorphismes entre la realisation de Betti tangentielle et la realisation de De Rham resulte en un enonce du type Kontsevich–Zagier fonctionnel purement algebrique et nettement plus satisfaisant que l’enonce obtenu dans [5].In this short note, we remark that a small modification in the computation made in [5] of the algebra of the torsor of isomorphisms between the tangential Betti realisation and the De Rham realisation results in a statement of functional Kontsevich–Zagier type which is purely algebraic and much more satisfactory than the statement obtained in [5].","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42523035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the curvature of the Fefferman metric of contact Riemannian manifolds","authors":"M. Nagase","doi":"10.2748/tmj/1568772179","DOIUrl":"https://doi.org/10.2748/tmj/1568772179","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45659248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hamiltonians are 2-by-2 positive semidefinite real symmetric matrix-valued functions satisfying certain conditions. In this paper, we solve the inverse problem for which recovers a Hamiltonian from the solution of a first-order system attached to a given Hamiltonian, consisting of ordinary differential equations parametrized by a set of complex numbers, under certain conditions for the solutions. This inverse problem is a generalization of the inverse problem for two-dimensional canonical systems.
{"title":"An inverse problem for a class of lacunary canonical systems with diagonal Hamiltonian","authors":"Masatoshi Suzuki","doi":"10.2748/tmj.20210816","DOIUrl":"https://doi.org/10.2748/tmj.20210816","url":null,"abstract":"Hamiltonians are 2-by-2 positive semidefinite real symmetric matrix-valued functions satisfying certain conditions. In this paper, we solve the inverse problem for which recovers a Hamiltonian from the solution of a first-order system attached to a given Hamiltonian, consisting of ordinary differential equations parametrized by a set of complex numbers, under certain conditions for the solutions. This inverse problem is a generalization of the inverse problem for two-dimensional canonical systems.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41605876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We describe transversely oriented foliations of codimension one on closed manifolds that admit simple foliated flows.
我们描述了闭合流形上余维1的横向叶理，允许简单的叶理流动。
{"title":"Simple foliated flows","authors":"J. '. L'opez, Y. Kordyukov, E. Leichtnam","doi":"10.2748/tmj.20201015b","DOIUrl":"https://doi.org/10.2748/tmj.20201015b","url":null,"abstract":"We describe transversely oriented foliations of codimension one on closed manifolds that admit simple foliated flows.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41735227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We establish pointwise growth estimates for the spherical derivative of solutions of the first order algebraic differential equations. A generalization of this result to higher order equations is also given. We discuss the related question of when for a given class $X$ of meromorphic functions in the unit disc, defined by means of the spherical derivative, and $m in mathbb{N} setminus {1}$, $f^min X$ implies $fin X$. An affirmative answer to this is given for example in the case of $mathord{rm UBC}$, the $alpha$-normal functions with $alphage1$ and certain (sufficiently large) Dirichlet type classes.
{"title":"Growth estimates for meromorphic solutions of higher order algebraic differential equations","authors":"S. Makhmutov, Jouni Rattya, Toni Vesikko","doi":"10.2748/tmj.20191118","DOIUrl":"https://doi.org/10.2748/tmj.20191118","url":null,"abstract":"We establish pointwise growth estimates for the spherical derivative of solutions of the first order algebraic differential equations. A generalization of this result to higher order equations is also given. We discuss the related question of when for a given class $X$ of meromorphic functions in the unit disc, defined by means of the spherical derivative, and $m in mathbb{N} setminus {1}$, $f^min X$ implies $fin X$. An affirmative answer to this is given for example in the case of $mathord{rm UBC}$, the $alpha$-normal functions with $alphage1$ and certain (sufficiently large) Dirichlet type classes.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42703127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This note is about the Chow ring of Verra fourfolds. For a general Verra fourfold, we show that the Chow group of homologically trivial $1$-cycles is generated by conics. We also show that Verra fourfolds admit a multiplicative Chow-K"unneth decomposition, and draw some consequences for the intersection product in the Chow ring of Verra fourfolds.
{"title":"Algebraic cycles and Verra fourfolds","authors":"R. Laterveer","doi":"10.2748/tmj/1601085625","DOIUrl":"https://doi.org/10.2748/tmj/1601085625","url":null,"abstract":"This note is about the Chow ring of Verra fourfolds. For a general Verra fourfold, we show that the Chow group of homologically trivial $1$-cycles is generated by conics. We also show that Verra fourfolds admit a multiplicative Chow-K\"unneth decomposition, and draw some consequences for the intersection product in the Chow ring of Verra fourfolds.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47302010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yingguo Li, A. Marciniak-Czochra, I. Takagi, Boying Wu
{"title":"Steady states of FitzHugh-Nagumo system with non-diffusive activator and diffusive inhibitor","authors":"Yingguo Li, A. Marciniak-Czochra, I. Takagi, Boying Wu","doi":"10.2748/TMJ/1561082598","DOIUrl":"https://doi.org/10.2748/TMJ/1561082598","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44687144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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